A while ago Joel Hamkins suggested that I copy cat this post of Norman’s: Chart of large cardinals near high-jump with my own large cardinal chart. So here is the large cardinal chart of Ramsey-like cardinals and their relationship to other large cardinal notions. The Ramsey-like cardinals: $\alpha$-*iterable* cardinals ($1\leq\alpha\leq\omega_1$), *strongly Ramsey* cardinals, *super Ramsey* cardinals, and *superlatively Ramsey* cardinals were introduced by myself and/or Philip Welch. All relevant definitions are here.

### Recent Writing

- A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
- A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails
- Computable processes which produce any desired output in the right nonstandard model
- Virtual large cardinals
- Virtual Set Theory and Generic Vopěnka’s Principle

### Mathoverflow Activity

- Comment by Victoria Gitman on Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?@Stefan For some reason, I cannot click on the link.Victoria Gitman
- Comment by Victoria Gitman on Cofinality of $j(\kappa)$ for a measurability embedding $j:V\to M$ with critical point $\kappa$@AsafKaragila I edited the question to make it clearer. Maybe I will ask your version as a follow-up if you don't ask it first :).Victoria Gitman
- Comment by Victoria Gitman on Cofinality of $j(\kappa)$ for a measurability embedding $j:V\to M$ with critical point $\kappa$@AsafKaragila I should have done a better job stating my question clearly. I wanted to know precisely what Yair answered: whether there are models where $\text{cf}(j(\kappa))$ is smaller than the size of $j(\kappa)$. Your interpretation of the question is very interesting as well, but I think much harder to answer.Victoria Gitman

- Comment by Victoria Gitman on Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
### Cantor’s Attic

- BerkeleyAdded that the critical point of j can be arbitrary large above kappa. Removing this notion results in a "Proto-Berkeley" cardinal. Source: http://logic.harvard.edu/blog/wp-content/uploads/2014/11/Deep_Inconsistency.pdf ← Older revision Revision as of 14:40, 23 June 2017 Line 1: Line 1: −A cardinal $\kappa$ is a ''Berkeley'' cardinal, if for any transitive set $M$ with $\kappa\in M$, there is […]Dan Saattrup Nielsen

- Berkeley

Yay! I love it!